Chevron and Exxon Mobil have both slipped more than 10 percent lower in the last year. West Texas Intermediate crude oil prices dropped 35 percent in that span.
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Gammel noted he has seen "a lot of volatility related to the oil price." Still, with Chevron's quarterly dividend at $1.07 per share and Exxon Mobil planning to increase its dividend to 73 cents per share, investors will still see returns on the stocks, he contended.
Jefferies has a "buy" rating on Chevron and a "hold" rating on Exxon. Gammel said he sees stronger production growth for Chevron than Exxon Mobil.
Chevron and Exxon Mobil were both down slightly in late trading Thursday.